Re: Assumptions ignored?

• To: mathgroup at smc.vnet.net
• Subject: [mg25097] Re: Assumptions ignored?
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Fri, 8 Sep 2000 03:00:43 -0400 (EDT)
• References: <8p9j95\$1fo@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Jos,

int = Integrate[x/Sqrt[x^2 + zp^2]^3, {zp, z, Infinity},
Assumptions -> {x > 0, z > 0}]

x*If[x^2 + z^2 >= 0 || Im[x^2] != 0,
(1 - (x*z*Sqrt[1 + z^2/x^2])/(x^2 + z^2))/x^2,
Integrate[(x^2 + zp^2)^(-3/2), {zp, z, Infinity}]]

I don't know why the assumptions are used further, but until they are we can
reassert them

Simplify[int, {x > 0, z > 0}]

(1 - z/Sqrt[x^2 + z^2])/x

Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Jos R Bergervoet" <Jos.Bergervoet at philips.com> wrote in message
news:8p9j95\$1fo at smc.vnet.net...
> With the following input:
>
>     Integrate[ x/Sqrt[x^2+zp^2]^3, {zp,z,Infinity},
>       Assumptions -> {x>0, z>0} ]
>
> I get:
>
>                   2    2             2
>     Out[1]= x If[x  + z  >= 0 || Im[x ] != 0,   ....
>
> Why does this if statement appear in the output? Why is Mathematica
> apparently ignoring my directive that x and z are positive?
>
> The same happens with Assumptions -> {x \[Element] Reals,
> z \[Element] Reals}  and with combinations of these two versions.
>
> I would like to have the plain answer (without ifs and whens) to
> use it in further computations. How can it be obtained? (If
> just the lines of input to be typed. I'm not very fond of GUI's ;-)
>
> Jos
>
> --
>   Dr. Jozef R. Bergervoet                      Electromagnetism and EMC
>   Philips Research Laboratories,             Eindhoven, The Netherlands
>   Building WS01                                     FAX: +31-40-2742224
>   E-mail: bergervo at natlab.research.philips.com    Phone: +31-40-2742403
>

```

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